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                黑白棋游戏                </h1>
                <p>时间限制：10s&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;  空间限制：128MB</p>			</div>
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                                <h3>题目描述</h3><p><div class="Section0" style="layout-grid:  15.6pt none">
<p class="p0" style="margin-top: 0pt; margin-bottom: 0pt"><span style="font-size: 12pt; font-family: '宋体'; mso-spacerun: 'yes'">黑白棋游戏是这样玩的：首先<font face="Times New Roman">GEN</font><font face="宋体">随机生成</font><font face="Times New Roman">N</font><font face="宋体">个</font><font face="Times New Roman">01</font><font face="宋体">序列，</font><font face="Times New Roman">0</font><font face="宋体">表示白棋，</font><font face="Times New Roman">1</font><font face="宋体">表示黑棋。接着两个人轮流按如下规则取棋：首先选取一个非空的</font><font face="Times New Roman">01</font><font face="宋体">序列，然后从该序列的左边开始连续取若干个棋子，这些被取的棋子中最多只能有一个黑棋，且该黑棋必需恰好是连续取的最后一个棋子，比如当前的序列为</font><font face="Times New Roman">001001</font><font face="宋体">，则可以取走的棋子有三种情况，分别为：</font><font face="Times New Roman">0</font><font face="宋体">，</font><font face="Times New Roman">00</font><font face="宋体">，</font><font face="Times New Roman">001</font><font face="宋体">。如果某人没有棋子可取了，则他负。</font></span><span style="font-size: 12pt; font-family: '宋体'; mso-spacerun: 'yes'"><o:p></o:p></span></p>
<p class="p0" style="margin-top: 0pt; margin-bottom: 0pt"><span style="font-size: 12pt; font-family: '宋体'; mso-spacerun: 'yes'">你通过特殊手段得到了<font face="Times New Roman">GEN</font><font face="宋体">生成时每一行生成的白棋数目和黑棋数目，由于不知道它们的排列情况，你做不到必胜，你只想知道你先手获胜的概率有多大</font><font face="Times New Roman">(</font><font face="宋体">假设你和你的对手都无限聪明</font><font face="Times New Roman">)</font><font face="宋体">。</font></span><span style="font-size: 12pt; font-family: '宋体'; mso-spacerun: 'yes'"><o:p></o:p></span></p>
<p class="p0" style="margin-top: 0pt; margin-bottom: 0pt"><span style="font-size: 12pt; font-family: '宋体'; mso-spacerun: 'yes'"><o:p></o:p></span></p>
<p class="p0" style="margin-top: 0pt; margin-bottom: 0pt"><span style="font-size: 12pt; font-family: 'Times New Roman'; mso-spacerun: 'yes'"><o:p></o:p></span></p>
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<!--EndFragment--></p><hr/><h3>输入格式</h3><p><p class="p0" style="margin-top: 0pt; margin-bottom: 0pt"><span style="font-weight: bold; font-size: 12pt; font-family: '宋体'; mso-spacerun: 'yes'"><o:p></o:p></span>&nbsp;</p>
<p class="p0" style="margin-top: 0pt; margin-bottom: 0pt"><span style="font-size: 12pt; font-family: '宋体'; mso-spacerun: 'yes'">第一行一个数<font face="Times New Roman">N</font><font face="宋体">。</font></span><span style="font-size: 12pt; font-family: '宋体'; mso-spacerun: 'yes'"><o:p></o:p></span></p>
<p class="p0" style="margin-top: 0pt; margin-bottom: 0pt"><span style="font-size: 12pt; font-family: '宋体'; mso-spacerun: 'yes'">第二行<font face="Times New Roman">N</font><font face="宋体">个数，第</font><font face="Times New Roman">i</font><font face="宋体">个数表示第</font><font face="Times New Roman">i</font><font face="宋体">个</font><font face="Times New Roman">01</font><font face="宋体">序列中黑棋的个数。</font></span><span style="font-size: 12pt; font-family: '宋体'; mso-spacerun: 'yes'"><o:p></o:p></span></p>
<p class="p0" style="margin-top: 0pt; margin-bottom: 0pt"><span style="font-size: 12pt; font-family: '宋体'; mso-spacerun: 'yes'">第三行<font face="Times New Roman">N</font><font face="宋体">个数，第</font><font face="Times New Roman">i</font><font face="宋体">个数表示第</font><font face="Times New Roman">i</font><font face="宋体">个</font><font face="Times New Roman">01</font><font face="宋体">序列中白棋的个数。</font></span><span style="font-size: 12pt; font-family: '宋体'; mso-spacerun: 'yes'"><o:p></o:p></span></p>
<p class="p0" style="margin-top: 0pt; margin-bottom: 0pt"><span style="font-size: 12pt; font-family: '宋体'; mso-spacerun: 'yes'"><o:p></o:p></span></p>
<p class="p0" style="margin-top: 0pt; margin-bottom: 0pt"><span style="font-size: 12pt; font-family: 'Times New Roman'; mso-spacerun: 'yes'"><o:p></o:p></span></p></p><hr/><h3>输出格式</h3><p><p class="p0" style="margin-top: 0pt; margin-bottom: 0pt"><span style="font-size: 12pt; font-family: '宋体'; mso-spacerun: 'yes'">仅一行，一个保留<font face="Times New Roman">6</font><font face="宋体">为小数的的实数表示先手获胜的概率。</font></span><span style="font-size: 12pt; font-family: '宋体'; mso-spacerun: 'yes'"><o:p></o:p></span></p>
<p class="p0" style="margin-top: 0pt; margin-bottom: 0pt"><span style="font-size: 12pt; font-family: '宋体'; mso-spacerun: 'yes'"><o:p></o:p></span></p>
<p class="p0" style="margin-top: 0pt; margin-bottom: 0pt"><span style="font-size: 12pt; font-family: 'Times New Roman'; mso-spacerun: 'yes'"><o:p></o:p></span></p></p><hr/><h3>样例输入</h3><pre>1

1

1


</pre><hr/><h3>样例输出</h3><pre>0.500000
</pre><hr/><h3>提示</h3><p><p></p>
<p><br />
样例解释</p>
<p>若生成序列为01，则先手必胜；若生成序列为10，则后手必胜。</p>
<p>两种情况出现的概率均为0.5，故先手获胜的概率为0.5。</p>
<p>0&lt;=每行的黑棋个数&lt;=100</p>
<p>0&lt;=每行的白棋个数&lt;=100</p>
<p>1&lt;=N&lt;=50</p>
<p>数据保证每个序列至少有一个棋子。<br />
</p></p><hr/><h3>题目来源</h3><p>没有写明来源</p>
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